Microlithographic projection exposure methods are used for fabricating semiconductor components and other finely structured components. Use is made of masks (reticles) that bear the pattern of a structure to be imaged, for example a line pattern of a layer of a semiconductor component, such as an integrated circuit (IC). A mask is positioned in a projection exposure system between an illumination system and projection objective in the region of the object surface of the projection objective, and illuminated with illumination radiation provided by the illumination system. The radiation varied by the mask and the pattern forms projection radiation propagating through the projection objective, which images the pattern of the mask onto the substrate to be exposed, which normally bears a radiation-sensitive layer (photoresist). In some cases, the pattern of the mask is illuminated with radiation from an effective source having an intensity distribution at a pupil plane of the illumination system corresponding to a particular illumination mode. An image of the illuminated mask is projected onto a resist-coated semiconductor wafer.